Large Deviation Principles of Invariant Measures of Stochastic Reaction-Diffusion Lattice Systems
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909189483266048 |
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| author | Wang, Bixiang |
| author_facet | Wang, Bixiang |
| contents | In this paper, we study the large deviation principle of invariant measures of stochastic reaction-diffusion lattice systems driven by multiplicative noise. We first show that any limit of a sequence of invariant measures of the stochastic system must be an invariant measure of the deterministic limiting system as noise intensity approaches zero. We then prove the uniform Freidlin-Wentzell large deviations of solution paths over all initial data and the uniform Dembo-Zeitouni large deviations of solution paths over a compact set of initial data. We finally establish the large deviations of invariant measures by combining the idea of tail-ends estimates and the argument of weighted spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02720 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Large Deviation Principles of Invariant Measures of Stochastic Reaction-Diffusion Lattice Systems Wang, Bixiang Probability Dynamical Systems 60F10, 60H10, 37L55, 37L30 In this paper, we study the large deviation principle of invariant measures of stochastic reaction-diffusion lattice systems driven by multiplicative noise. We first show that any limit of a sequence of invariant measures of the stochastic system must be an invariant measure of the deterministic limiting system as noise intensity approaches zero. We then prove the uniform Freidlin-Wentzell large deviations of solution paths over all initial data and the uniform Dembo-Zeitouni large deviations of solution paths over a compact set of initial data. We finally establish the large deviations of invariant measures by combining the idea of tail-ends estimates and the argument of weighted spaces. |
| title | Large Deviation Principles of Invariant Measures of Stochastic Reaction-Diffusion Lattice Systems |
| topic | Probability Dynamical Systems 60F10, 60H10, 37L55, 37L30 |
| url | https://arxiv.org/abs/2405.02720 |